Lecture 9: Debt Markets and Term Structure
Discount Bonds • No coupon payments, just principal at maturity date (conventionally, $100). • Initially sold at a discount (less than $100) and price rises through time, creating income. • Term T, Yield to Maturity (YTM) r
Compound Interest • If annual rate is r, compounding once per year, balance = (1+r)t after t years. • If compounded twice per year, balance is (1+r/2)2 t after t years. • If compounded n times per year, balance is (1+r/n)nt after t years. • Continuous compounding, balance is ert.
Price & Yield on T-Bills • For buyer, Price = 100 -Discount • Discount = asked*(Days to Maturity/360). • Yield = (Discount/Price)(365/(Days to Maturity)). (Unless maturity > 6 months, in which case quadratic formula using semiannual compounding is required. )
Example Dec 18, 2000 • T-Bill maturing March 15, Asked=5. 83%, 87 days to maturity. • Discount = 5. 83*87/360=1. 40891 • Price=100 -1. 40891=98. 59108 • Yield=(1. 40891/98. 59108)(365/87)=5. 995%
Conventional Bonds Carry Coupons • Conventional Bond Issued at par (100), coupons every six months. • Term is time to maturity.
Bond Yield Tables
Term Structure of Interest Rates • • • Yield to maturity plotted against term Also called “The Yield curve” Usually upward sloping Inverted yield curve Hump shaped yield curve
Term Structure of Interest Rates, 1999 and 2004
Causes of Interest Rates • Eugen von Böhm-Bawerk: Capital and Interest, 1884: technological progress, time preferences, advantages to roundaboutness • Irving Fisher 1867 -1947, wrote Theory of Interest 1930
Irving Fisher Yale ‘ 88
Irving Fisher Diary at Yale • July 31, 1885 “it is neither politic nor right to study at the expense of one’s health. ” Rowing. • “When I fall in love she must be a girl of pure morality, broad culture and fine tastes. ” • “I have an earnest desire to be good and useful” • April 4, 1886, roommate dies of a “cold. ” • May 29, 1887, “I take great satisfaction in my election to Bones for I felt it to be my first little conquest among men. As a freshman I was afraid of my own voice. ”
Irving Fisher Diagram Today
Forward Rates • Forward rates are interest rates that can be taken in advance using term structure • J. R. Hicks Value and Capital 1939
Example of Forward Rates • Suppose I in 1925 expect to have £ 100 to invest in 1926, but want the money back by 1927. How can I guarantee the interest rate on the £ 100 investment today (1925)? • Buy in 1925 (1+r 2 )2/(1+r 1) 2 -period discount bonds maturing at £ 100 in 1927. Cost: £ 1/(1+r 1) • Short in 1925 one 1 -period discount bond maturing at £ 100 in 1926. Receive: £ 1/(1+r 1) • I have now locked in the interest rate 1+f=(1+r 2)2/ (1+r 1) between 1926 and 1927.
Expectations Theory • Forward rates equal expected spot rates • Slope of term structure indicates expected future change in interest rates.
Liquidity Preference Hypothesis • Forward rates equal expected future spot rates plus a “risk premium. ” (J. R. Hicks, 1939) • Modigliani and Sutch: Risk premium could be either positive or negative. Preferred habitat hypothesis
Inflation and Interest Rates • Nominal rate quoted in dollars, real rate quoted market baskets • Nominal rate usually greater than real rate.
Indexed Bonds • Paul Revere, Massachusetts, 1780 • U. S. Treasury, 1997 • TIPS Treasury Inflation Protection Securities, $115 billion outstanding 2000, 2% of US national debt • UK Index-Linked Gilts 20% of debt • France recently issued Euro Index bonds
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